What are the divisors of 1446?

1, 2, 3, 6, 241, 482, 723, 1446

There is a total of 8 positive divisors.
The sum of these divisors is 2904.
The arithmetic mean is 363.

4 even divisors

2, 6, 482, 1446

4 odd divisors

1, 3, 241, 723

How to compute the divisors of 1446?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 1446 by each of the numbers from 1 to 1446 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

1446 / 1 = 1446 (the remainder is 0, so 1 is a divisor of 1446)
1446 / 2 = 723 (the remainder is 0, so 2 is a divisor of 1446)
1446 / 3 = 482 (the remainder is 0, so 3 is a divisor of 1446)
...
1446 / 1445 = 1.0006920415225 (the remainder is 1, so 1445 is not a divisor of 1446)
1446 / 1446 = 1 (the remainder is 0, so 1446 is a divisor of 1446)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 1446 (i.e. 38.026306683663). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

1446 / 1 = 1446 (the remainder is 0, so 1 and 1446 are divisors of 1446)
1446 / 2 = 723 (the remainder is 0, so 2 and 723 are divisors of 1446)
1446 / 3 = 482 (the remainder is 0, so 3 and 482 are divisors of 1446)
...
1446 / 37 = 39.081081081081 (the remainder is 3, so 37 is not a divisor of 1446)
1446 / 38 = 38.052631578947 (the remainder is 2, so 38 is not a divisor of 1446)